Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> coll;
  for (int i = 1;; i++) {
    int tmp;
    coll.push_back(tmp = i * (i + 1) / 2);
    if (tmp >= n) break;
  }
  bool f = false;
  for (int i = coll.size() - 1; i >= 0; i--) {
    if (coll[i] < n) {
      int s = n - coll[i], k = i;
      for (int j = 0; j <= k; j++)
        if (s - coll[j] == 0) {
          f = true;
          break;
        }
    }
    if (f) break;
  }
  if (f)
    cout << "YES";
  else
    cout << "NO";
  return 0;
}